Figure 2: Band geometry and gap data for the augmented Haldane model.

(a) Band geometry over the reciprocal lattice unit cell spanned by b₁, b₂, for parameter values maximizing the gaps and minimizing σ_B. Axes of ellipses are proportional to the eigenvectors of the quantum metric g^α(k). Ellipse colour is given by the relative deviation of Berry curvature B_α(k) from its Brillouin zone-averaged value. (b) Berry curvature fluctuations σ_B and (c) Brillouin zone-averaged trace inequality as a function of couplings t₂, t₃, where we set t₁=1 and φ=π/2 in this and remaining panels without loss of generality. (d) Gap Δ as a function of couplings for the bosonic Laughlin state of N=8 bosons at v=1/2. (e) Gap as a function of couplings for the bosonic Moore–Read state of N=10 bosons at v=1.